Stress influence Charts for transversely isotropic rocks

Abstract

A graphical procedure to calculate stresses in a transversely isotropic half-space subjected to a three-dimensional surface load has been developed. The surface load can be distributed on an irregularly-shaped area. The planes of transverse isotropy are assumed to be parallel to the horizontal surface of the half-space. The closed-form solutions for stresses at a point under the vertex of a loading sector, with a unit load intensity are presented first. Based on these solutions, five influence charts are constructed for calculating the six components of a stress tensor at any given point in the half-space. The charts are composed of unit blocks. Each unit block is bounded by two adjacent radii and arcs, and contributes the same level of influence to the stress within the half-space. An example is presented to demonstrate the use of the new graphical method . For the case analyzed, results from the new graphical method agree with those of analytical solutions within 3%. The new influence charts can be a practical alternative to the existing analytical or numerical solutions, and provides results with reasonable accuracy.